Geodesic
Covariant hydrodynamics of Hamiltonian systems
Dalʹnevostočnyj matematičeskij žurnal, Tome 21 (2021) no. 2, pp. 166-179

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The theory of hydrodynamic reduction of non-autonomous Hamiltonian mechanics (V. Kozlov, 1983) is presented in the geometric formalism of bundles over the time axis $R$. In this formalism, time is one of the coordinates, not a parameter; the connections describe reference frames and velocity fields of mechanical systems. The equations of the theory are presented in a form that is invariant with respect to time-dependent coordinate transformations and the choice of reference frames. 
@article{DVMG_2021_21_2_a3,
     author = {A. I. Gudimenko},
     title = {Covariant hydrodynamics of {Hamiltonian} systems},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {166--179},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2021_21_2_a3/}
}
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A. I. Gudimenko. Covariant hydrodynamics of Hamiltonian systems. Dalʹnevostočnyj matematičeskij žurnal, Tome 21 (2021) no. 2, pp. 166-179. http://geodesic.mathdoc.fr/item/DVMG_2021_21_2_a3/